This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The PI investigates the structure of minimal sets in topological dynamical systems and foliations that serve as counterexamples to the Seifert Conjecture and the Modified Seifert Conjecture. The interesting properties of these minimal sets are the topological dimension, the Hausdorff dimension, isolation, and Czech homology in relation to shape theory. Dynamics is also employed in work on problems in discrete and computational geometry.
Dynamical systems impact other areas of science. The study of minimal sets is an extension of the study of fixed points and attractors. The theory has application to biology, population research, and economy, in addition to the traditional Science Technology Engineering and Mathematics (STEM) fields. The geometry problems studied by the PI have applications to medical imaging.
